Scenario for questions 1-4: A quality control engineer plans…
Scenario for questions 1-4: A quality control engineer plans a study to assess the impact of storage on the sweetness of a new cola. Ten trained tasters are available to rate the cola’s sweetness on a 10-point scale before and after storage, so that each taster’s judgement of the change of sweetness can be assessed. Industry records indicate that sweetness change scores vary from taster to taster according to Normal distribution with mean μ and standard deviation about σ=1. Suppose the sample mean of the sweetness change from the ten tasters is \( \bar{x}=-0.5. \)(Note that negative means sweetness loss, and positive means sweetness gain.) To see if the taste test gives reason to think that the cola does change sweetness, the engineer will test
Read DetailsCardanol, an agricultural byproduct of cashew nut shells, is…
Cardanol, an agricultural byproduct of cashew nut shells, is a cheap and abundantly available renewable resource. Researchers investigated the use of cardanol as an additive for natural rubber. Cardanol was grafted onto pieces of natural rubber latex, and the chemical properties were examined. One property of interest is the grafting efficiency (measured as a percentage) of the chemical process. The researchers manipulated several independent variables in the chemical process – x1 = initiator concentration (part per hundred resin), x2=cardanol concentration (parts per hundred resin), x3=reaction temperature (degrees Centigrade) and x4=reaction time (hours). Values of these variables, as well as the dependent variable y=grafting efficiency, were recorded for a sample of n=9 chemical runs. The data are provided in the accompanying table. A Minitab output of the first order model, is also shown. Answer the below questions in details. (a) [10 points] Conduct a test of overall model adequacy. Use α=0.10. (b) [10 points] Practically interpret the value of Ra2. (c) [10 points] Practically interpret the value of s. (d) [10 points] Find and interpret a 90% confidence interval for β3. (e) [10 points] Conduct a test of H0: β4=0. What do you conclude?
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